I'm a regular user of Canon's Digital Photo Professional 4 and I've never noticed any such way to do click on a spot to automatically do it.

Perhaps an easier way to identify when a particular spot is at a certain luminance level is to enable 'Show highlight/shadow warning'. This can be done via the 'Preview' menu, by clicking on the "curves" symbol with an exclamation point at the bottom of the edit pane, or by using keyboard shortcut 'Alt + M'.

You can then set the parameters of the highlight/shadow warning via 'Menu → Tools → Highlight/shadow warning display settings...' or the dropdown menu attached to the right side of the "curves" symbol with exclamation at the bottom of the edit pane.

By setting the highlight threshold to '250', any area of the image with an average (all three colors combined) value of 250 or higher will be displayed using the warning color selected in the settings. Default colors are blue for shadows and red for highlights, but you can change them to any of 48 preset or 12 custom colors.

Once you've got the highlight/shadow warning display set up, adjusting brightness, either by using the slider or, even better, the left and right arrows when the brightness slider is active will change the areas that show the warning. It's a little easier to watch the image as you press the right arrow until the spot your curser is hovering over turns red.

Would be nice to have an option to do it automatically at the same time when adjusting/clicking white balance on some spot.

Regarding using the same point to set a maximum value and to set white balance, in general you don't want to use areas that are near saturation to set white balance automatically. If one (or two) channels are fully saturated and the other(s) are not, your results will not be accurate. It's better to use a neutral mid-tone to set white balance. That's why gray cards are "18%" gray that should display as (127,127,127) when "properly" exposed.